A farmer can produce 10,000 pears on his one acre farmland.When he uses the same land for apple cultivation,a total of 5,000 apples can be produced.He realizes that with the introduction of a new fertilizer,he can increase the maximum production of apples to 7,000.The maximum production of pears,however,remains unchanged.Given that his production possibility frontier (PPF)is linear and apples are graphed on the Y-axis and pears on the X-axis,calculate the slope of his PPF.

Question

Quizplus · Accepted Answer

The slope of the PPF is calculated by taking the change in the quantity of apples produced (the Y-axis) over the change in the quantity of pears produced (the X-axis). Initially, the farmer can produce 5,000 apples or 10,000 pears. With the new fertilizer, he can produce 7,000 apples, but the production of pears remains unchanged at 10,000. The change in apples is 7,000 - 5,000 = 2,000, and the change in pears is 0 since the maximum production of pears does not change. However, to find the slope, we consider the trade-off between producing apples and pears. Moving from 10,000 pears to 0 pears allows for an increase from 5,000 to 7,000 apples. Thus, the slope is calculated as the change in apples (2,000) over the change in pears (-10,000), which is -2,000 / 10,000 = -0.2. However, this explanation mistakenly calculates the slope based on an incorrect interpretation of the change in pears. The correct approach is to consider the entire range of production possibilities. Given the linear PPF and the points (10,000, 0) for pears and (0, 7,000) for apples, the slope is (0 - 7,000) / (10,000 - 0) = -7,000 / 10,000 = -0.7.

A Farmer Can Produce 10,000 Pears on His One Acre